Theorems · Theorem · commutative algebra

PowerBasis.quotientEquivQuotientMinpolyMap_apply_mk

∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (pb : PowerBasis R S)
  (I : Ideal R) (g : Polynomial R),
  (pb.quotientEquivQuotientMinpolyMap I)
      ((Ideal.Quotient.mk (Ideal.map (algebraMap R S) I)) ((Polynomial.aeval pb.gen) g)) =
    (Ideal.Quotient.mk (Ideal.span {Polynomial.map (Ideal.Quotient.mk I) (minpoly R pb.gen)}))
      (Polynomial.map (Ideal.Quotient.mk I) g)

Defined in

Mathlib.RingTheory.AdjoinRoot

Cited by

0 results in Mathlib

Foundations

Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebra